Question

In a cricket tournament every team played only once with the other team. In a total $153$ matches are held. How many teams participated in the tournament?

• A. $15$
• B. $16$
• C. $17$
• D. $18$

Answer 1

The correct option is D $18$

Let the number of team be $x$

In order to play a game two teams are needed

Number of games

${\Rightarrow }^x{C}_2$

Given number of games $=153$

${\Rightarrow }^x{C}_2=153\Rightarrow \frac{x(x-1)}{2}=153\Rightarrow x(x-1)=306\Rightarrow x=18orx=-17$

Therefore number of participants cannot be negative

$\Rightarrow x=18$